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De verkoopcijfers van auto's

*Unverified author*
R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Thu, 27 May 2010 12:22:32 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/May/27/t1274963056ct0llmevr09urvd.htm/, Retrieved Thu, 27 May 2010 14:24:17 +0200
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/May/27/t1274963056ct0llmevr09urvd.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
KDGP2W62
 
Dataseries X:
» Textbox « » Textfile « » CSV «
68897 38683 44720 39525 45315 50380 40600 36279 42438 38064 31879 11379 70249 39253 47060 41697 38708 49267 39018 32228 40870 39383 34571 12066 70938 34077 45409 40809 37013 44953 37848 32745 43412 34931 33008 8620 68906 39556 50669 36432 40891 48428 36222 33425 39401 37967 34801 12657 69116 41519 51321 38529 41547 52073 38401 40898 40439 41888 37898 8771 68184 50530 47221 41756 45633 48138 39486 39341 41117 41629 29722 7054 56676 34870 35117 30169 30936 35699 33228 27733 33666 35429 27438 8170 62557
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.294870697455103
beta0
gamma0.335511814386048


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137024971014.3015814803-765.301581480278
143925339703.6268082511-450.626808251065
154706047620.1628926628-560.162892662767
164169741970.8422031604-273.842203160399
173870838645.108077761862.891922238181
184926748936.740287549330.259712451036
193901839927.344520585-909.344520585044
203222835294.5427433688-3066.54274336876
214087040022.9121377387847.087862261258
223938335879.41468000443503.58531999561
233457130989.10602358413581.89397641593
241206611505.5372144255560.462785574548
257093871920.8782040774-982.878204077395
263407740171.8003070546-6094.80030705463
274540946173.4577239264-764.457723926447
284080940686.3018647619122.698135238097
293701337638.4924524002-625.492452400198
304495347459.781724517-2506.78172451699
313784837772.904467190575.0955328094569
323274533102.5281638041-357.528163804076
334341239422.56119247313989.43880752695
343493136799.3932356376-1868.39323563762
353300830547.68481107672460.31518892329
36862011062.1518262835-2442.15182628345
376890662794.05359643496111.94640356513
383955634971.5034770114584.49652298904
395066945231.25268896015437.74731103993
403643241666.9976341778-5234.99763417777
414089136910.66741890833980.33258109174
424842847836.9858478707591.014152129268
433622239337.2966219577-3115.2966219577
443342533547.8765998168-122.876599816846
453940141074.9660311752-1673.96603117516
463796735507.61495105252459.38504894752
473480131487.58088231543313.41911768465
481265710644.38453327452012.61546672553
496911673910.5935551122-4794.59355511224
504151939543.55760271621975.4423972838
515132149857.80504585551463.19495414446
523852942204.0291188827-3675.02911888271
534154740002.51722085661544.48277914341
545207349740.33833562192332.66166437809
553840140411.0985281166-2010.09852811658
564089835423.53627185445474.46372814564
574043945002.3170290945-4563.31702909454
584188839201.22837299622686.77162700382
593789835038.38799820732859.61200179267
60877111975.9237638124-3204.92376381236
616818468503.046550077-319.046550076993
625053038345.068366553512184.9316334465
634722151867.2284269123-4646.22842691231
644175641198.6804452804557.319554719601
654563341481.28749434034151.71250565973
664813852607.778993799-4469.77899379899
673948640171.5547271417-685.554727141694
683934137247.30868623232093.69131376772
694111743352.2661640744-2235.26616407436
704162939932.99911576081696.00088423921
712972235526.4441982979-5804.44419829791
72705410314.2408547113-3260.24085471126
735667662287.7597579446-5611.75975794459
743487036352.8819143467-1482.88191434673
753511740637.7685070525-5520.7685070525
763016932621.1230168432-2452.12301684317
773093632601.4141913804-1665.4141913804
783569937842.7973402739-2143.79734027387
793322829616.45037597353611.54962402645
802773329066.4756103698-1333.47561036981
813366631982.0502648531683.94973514697
823542931046.37524108644382.62475891363
832743826978.3818160336459.618183966417
8481707906.20965555718263.790344442824
856255756671.50521445055885.49478554955


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8635451.150837307531927.633201859938974.6684727551
8739151.342863950335016.200055934943286.4856719656
8833260.638432154428949.685553922337571.5913103864
8934204.079011988829404.81128746539003.3467365126
9040262.59206345134559.805989137845965.3781377641
9133401.049092861228019.221643865138782.8765418572
9230451.392942887825026.389454082435876.3964316932
9334770.820896014428468.604759503341073.0370325255
9433892.344252809527401.281848799440383.4066568195
9527507.071509610421623.340310561133390.8027086598
968051.469323409654223.1482921964911879.7903546228
9758059.15754621140259.082023804875859.2330686172
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/May/27/t1274963056ct0llmevr09urvd/1wijj1274962948.png (open in new window)
http://www.freestatistics.org/blog/date/2010/May/27/t1274963056ct0llmevr09urvd/1wijj1274962948.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/May/27/t1274963056ct0llmevr09urvd/2wijj1274962948.png (open in new window)
http://www.freestatistics.org/blog/date/2010/May/27/t1274963056ct0llmevr09urvd/2wijj1274962948.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/May/27/t1274963056ct0llmevr09urvd/37rim1274962948.png (open in new window)
http://www.freestatistics.org/blog/date/2010/May/27/t1274963056ct0llmevr09urvd/37rim1274962948.ps (open in new window)


 
Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
 
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
 
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
 




Copyright

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa


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